Question

Starting from rest a model rocket accelerates upwards at 24 m/s. How long does it take to reach a height of 192 meters

Answer 1

`t=4s`

Step-by-step explanation:

We want to write the equation of displacement (vertical in this case) for accelerated motion, which is
`y=y_0+v_yt+(a_yt^2)/(2)`. If we take the upward direction as positive, assume it starts from rest and from the ground, and
`a_y=24m/s^2` (the units are wrong in the text, if accelerates at that magnitude, it's an acceleration, in particular in
`m/s^2`), then we have
`y=(12m/s^2)t^2`.

We want to know the time when
`y=192m`, so we need to solve
`192m=(12m/s^2)t^2`, for which we have:

`t=\sqrt{(192m)/(12m/s^2)}=4s`

This means it takes 4 seconds for a rocket accelerating at
`24m/s^2` to reach a height of 192m.